**Estimating stratospheric aerosols physical properties**

**by Ruby-lidar observations**

G. P. GOBBI(*)

*Istituto di Fisica dell’Atmosfera, Consiglio Nazionale delle Ricerche*
*Via Fosso del Cavaliere 100, 00133 Roma, Italy*

(ricevuto il 12 Settembre 1997; revisionato il 6 Aprile 1998; approvato il 27 Aprile 1998)

**Summary. — An optical model originally developed at 532 nm is applied to the Ruby**
laser wavelength of 694 nm. Functional relationships resulting from the model allow
estimates of stratospheric aerosol surface area, volume, extinction-to-backscatter ratio,
extinction, and effective radius from single wavelength, Ruby-lidar measurements.
These parametrizations are valid for global stratospheric sulphate aerosols and
liquid polar stratospheric clouds. Relative errors of the estimates are in the range of
15–45% for surface area, 15–30% for volume, 20–35% for
extinction-to-backscatter ratio and extinction, and 40–55% for effective radius. These errors are
*comparable to the ones characterizing direct, in situ techniques as optical particle*
counters. Comparisons with results of the original model at 532 nm are presented.
PACS 94.10.Gb – Absorption and scattering of radiation.

PACS 92.60.Mt – Particles and aerosols. PACS 42.68 – Atmospheric Optics.

**1. – Introduction**

Stratospheric aerosols participate in the control of factors, such as global warming and cooling, chemistry of the ozone layer and atmospheric dynamics [1-3]. Their action maximizes after major volcanic eruptions and lasts for several years thanks to long decay times [1]. Conversely, the very low temperatures reached in the winter polar regions lead to the growth of background sulphate aerosols by condensation of ambient nitric acid and water [2]. The resulting optically thin clouds, known as polar stratospheric clouds (PSC), represent a seasonal, colder equivalent of volcanic aerosols. Thanks to their large surface area and settling speeds, PSC set up the conditions for the springtime “ozone hole” phenomenon, by both activating ozone-destroying halogens and sedimenting halogen-capturing nitrates [2]. In a similar fashion, volcanic

(*) E-mail: gobbiHsunifa1.ifsi.rm.cnr.it

aerosols enhance both ozone photodissociation and heterogeneous activation of ozone-depleting species, two processes resulting into a global, long-lasting ozone reduction [3]. The background stratospheric aerosol layer peaks at approximately 70 hPa and is formed by diluted sulphuric-acid droplets which remain supercooled, therefore spherical, down to at least 192 K [4-6]. In typical mid-latitude conditions, stratospheric aerosols are composed of 70–75% H2SO4 by weight, while in the colder high-latitude

stratosphere they deliquesce to approximately 50% H2SO4-50% H2O [7-9]. Below

*approximately 192 K, i.e. in polar winter conditions, ambient nitric acid condenses onto*
sulphate aerosols to form supercooled ternary solution (STS) PSC, which can remain
liquid down to the ice frost point temperature [10]. The assumption of sphericity holds
then for all these aerosols, whose scattering properties can be computed by means of
the Mie theory.

This paper presents results obtained at the Ruby laser wavelength of 694 nm, by a model originally developed to estimate aerosols physical properties from Nd-YAG lidar returns at 532 nm [11]. Interest for the Ruby laser wavelength is justified by the large number of such lidars still in operation. On the basis of that model, functional relationships linking single-wavelength lidar backscatter at 694 nm to aerosols surface area, volume, extinction-to-backscatter ratio, extinction, and effective radius will be obtained. These results will be compared to the ones obtained at 532 nm. The methodology of the study will be presented in the next two sections. For a more complete description of the optical model the reader is referred to [11].

**2. – Aerosol physical and optical properties**

The atmospheric backscatter of lidar pulses is generated by the combined effect of
*molecular b*m *and aerosols b*a backscatter cross-sections [12]. Typical 532 nm,

*mid-latitude values for b*mat 15, 18 and 25 km are of the order of 2.5 31029, 1.6 31029,

and 5.3 310210_{cm}21_{sr}21_{, respectively [11]. While stratospheric background aerosols}

*cross-sections at 532 nm hardly exceed b*a4 10210cm21 sr21, volcanic aerosols and

STS PSC span the region 1029_{–10}28 _{cm}21_{sr}21 _{and heavy volcanic and ice PSC can}

*grow in excess of b*a4 1028 cm21sr21. Typical lidar-detectable aerosol backscatter is

*of the order of b*aB 10211cm21 sr21*[11]. In lidar analysis, the scattering ratio R 4*

*(b*a*1b*m*) Ob*m is commonly employed to represent the aerosol contribution to the total

*backscatter, R 41 indicating an aerosol-free atmosphere. At 532 nm, the 18 km *
*back-ground aerosol layer shows then typical values of R B1.06. This is to be compared to*
*maximum post-Pinatubo observations of RB100 at 25 km in the tropics [13] and RB10*
*at midlatitude [14]. In the case of PSC, STS attain scattering ratios of up to R B4-5,*
*while ice ones can reach values of the order of R B100 [15]. As for increasing*
*wavelengths the molecular backscatter decreases much faster than the aerosol one, R*
*at 694 nm is larger than at 532 nm. Typical values of R at 694 nm will be derived in the*
next sections.

*At the wavelength l , the backscatter efficiency Q*bs*(r , l , m) and the extinction*

*efficiency Q*ext*(r , l , m) of homogeneous, spherical particles of radius r and complex*

*refractive index m 4m*re*2 im*im can be computed by means of the Mie theory. The

*aerosol backscatter cross-section per unit air volume b*a, is then obtainable as

*b*a4

Q

*Q*bs*(r , l , m) n(r) pr*2*dr ,*

*where n(r) is the particle size distribution. In a similar way, the extinction cross-section*

*s*a *can be computed by replacing Q*bs *by Q*ext in eq. (1). Knowledge of the aerosol

*extinction-to-backscatter ratio R*eb*4 s*a*Ob*a is fundamental to the correction for

extinction in the inversion of lidar profiles and to the cross comparison of lidar and satellite extinction observations [11].

Many curves have been employed to fit the size distribution of stratospheric aerosols: gamma, lognormal, power law, etc. [16]. The lognormal, reported below, is often used because it well reproduces the bell-shaped dispersion (in log-log coordinates) of observed aerosol distributions [17]:

*n(r) 4* *dn*
*dr* 4
*N*0
*r*k*2 p ln s*g
exp

## y

2 ln 2*(rOr*g) 2 ln2

*g)*

_{(s}## z

. (2)*In eq. (2), N*0 *indicates the total number of particles per unit volume, r*g *and s*g the

distribution geometric radius and width, respectively. Typical background aerosol distributions at 18-20 km are well fitted by a monomodal lognormal with parameters

*N*04 10 cm23*, r*g*4 0.0725 mm, and s*g4 1.86 [18]. Volcanic injections perturb

back-ground conditions by generating large amounts of sulphuric acid which both condenses onto pre-existing aerosols and homogeneously nucleates fine, fast-coagulating particles. These processes often involve the buildup of bimodal distributions, characterized by a large-particle mode in the micron-size range. Bimodality is commonly observed after major volcanic eruptions [19-21, 17], and must be considered when evaluating aerosol optical properties [11].

**3. – Aerosol scattering model**

*The aim of this paper is to provide relationships between b*aat 694 nm and aerosols

*parameters as total surface area S*a*, volume V*a*, extinction-to-backscatter ratio R*eb4

*s*a*Ob*a*, extinction s*a*, and effective radius r*eff. The latter parameter, defined as

*r*eff4

*n(r) rpr*2

*dr*0 Q

*n(r) pr*2

*(3)*

_{dr}was not considered in [11], but is often employed for characterizing a distribution
typical size [9]. As proceeded in the 532 nm case [11], this aim is pursued via a statistical
*approach, i.e. evaluating such relationships by means of the Mie theory for a large*
number of aerosol size distributions, representative of conditions ranging from
background to postvolcanic. Functional links between these variables are then found
on the basis of the average values of the dispersion of computed relationships. As the
number of observations of real size distributions is limited, the problem is approached
*using a Monte Carlo technique, i.e. generating random distributions and compositions*
whose parameters are constrained within experimentally observed boundaries.
According to previous considerations, distributions are chosen to be monomodal and
bimodal lognormals. Referring to the first and second mode by subscripts 1 and 2,
*respectively, six parameters (N*1*, r*1*, s*1*, N*2*, r*2*, and s*2*) plus real (m*re) and imaginary

TABLE *I. – Minimum and maximum values bounding the random variability of distribution*

*parameters employed in simulations.*

Run *N*1( cm23) *r*1( cm23) *s*1 *N*2( cm23)
694
532
1.0 30.0
1.0 30.0
2.0 Q 1026 _{4.0 Q 10}25
2.0 Q 1026 _{4.0 Q 10}25
1.3 2.3
1.3 2.3
1.0 Q 1024 _{4.0}
1.0 Q 1024 _{4.0}
Run *r*2( cm23) *s*2 *m*re *m*im
694
532
1.5 Q 1025 _{3.0 Q 10}24
1.5 Q 1025 _{3.0 Q 10}24
1.1 1.8
1.1 1.8
1.410 1.450
1.420 1.460
20.0 21.0 Q 1026
20.0 21.0 Q 1026

*(m*im) parts of the refractive index are randomly generated to compute each

distribution optical properties. Selection of boundaries and acceptance rules for the
generation of these parameters have been established on the basis of a large set of field
observations reported in the literature and described in [11]. In this way, all possible
distributions and compositions generated within the experimentally determined limits
are statistically represented in the simulations. This work will address the “reference”
aerosol case (run 99 in [11]), which was demonstrated to be the best model for
background to heavy volcanic sulphate aerosols and also for liquid PSC with refractive
*index m*re, varying between 1.37 and 1.5 (run 96, in [11]). Conversely, this model is not

representative of early volcanic conditions, when high supersaturation leads to the
homogeneous nucleation of large numbers of new particles [11]. However, these
*transient conditions extend only to the first 1-2 months after the eruption, i.e. until*
coagulation brings down the total number of particles to typical stratospheric
values [3, 22]. For comparison purposes, the 532 nm simulation will be run again and
presented. At both the 694 and 532 nm wavelengths, a new variability range of the
*refractive index as obtained from recent results reported by Russell et al. [9] will be*
employed. All boundaries to the variability of distribution parameters are summarized
in table I. Different runs are numbered according to the relevant wavelength. Ten
thousand distributions (2 000 more than in [11]) are considered in each simulation. For
*every distribution, b*a*and s*a*, S*a*, V*a*and r*eff are integrated over the radius range 0.001

*to 25 mm. Convergence of the integral is accepted when resulting better than 1/50 000.*

**4. – Model results**

**4**.*1. Aerosol surface area. – Average values and relative errors for the relationships*

*S*a*vs. b*a at the two wavelengths are presented in figs. 1a and 1b, respectively. In this

and the following cases, average values are computed at eight, equally spaced bins per
decade. To be considered in the analysis, such bins must include at least 100
distributions. Every average point is represented by one plotted symbol. Throughout
*the discussion, model errors will be referred to as the 1 s dispersion of the investigated*
*parameter (presently the aerosol surface area S*a) resulting from each simulation.

*Errors in the lidar evaluation of the independent variable b*aare expected to be much

smaller than the model ones (order of 2% as soon as aerosol grow). Since these errors also depend on system characteristics, they will not be considered in the model error analysis.

*Fig. 1. – (a): Average value points of the relationships S*a*vs. b*acomputed at 694 (open triangles)

and 532 nm (crossed circles). Solid lines show the log-log, second-order polynomial fit to the
*relevant points. Fit parameters are reported in table II. (b): Relative errors dS*a*OS*a*( dS*a*4 1 s) of*

*Backscatter cross-sections b*a obtained in run 694 range between 1 310212 and

2 31028_{cm}21 _{sr}21_{, spanning 4 orders of magnitude. At 532 nm, b}

a values range

between 2 310212 _{and 3 310}28_{cm}21_{sr}21_{. The largest cross-section aerosols achieved}

*within these boundaries can therefore account for a 532 nm scattering ratio R F10*
*upward of 15 km altitude and R B40 at 25 km. At 694 nm, due to the l*24_{-dependence of}

*molecular scattering, and to the approximate l*21_{-dependence of the aerosol}

*backscatter, this converts to scattering ratios R F20 upward of 15 km and to RB80 at*
*25 km. The relevant range for S*ais 1.5 310295 8 3 1027cm2cm23 *(0.15–80 mm*2cm23),

spanning almost 3 orders of magnitude. As found in [11], logarithmic-coordinates
*relationships S*a*, V*a*, and R*eb*vs. b*aare well approximated by a second-order polynomial

(parabolic) curve of the kind

*Y 4a0 Y1 a1 YX 1a2 YX*2,

(4)

*where X 4log b*a*and Y is the logarithm of the parameter investigated, in this case S*a.

*The corresponding equation to evaluate S*ais then

*S*a4 10*(a0 S1 a1 SX 1a2 SX*
2_{)}

. (5)

Least-squares parabolic fits to the runs average values and their relevant parameters

*a0 S, a1 S, and a2 S*are reported in fig. 1a as solid lines and in table II, respectively. The

range of backscatter cross-sections over which the fit is computed and the correlation
coefficient, representing the quality of the parabolic approximation, are also reported
in table II. Dispersion of results about their average value provides a further
*char-acterization of simulations. Figure 1b reports such relative errors dS*a*OS*a *( dS*a*4 1 s*

*dispersion of computed surface area values) vs. b*a, for the two cases presented in

*fig. 1a. These plots are representative of the accuracy of the model at estimating S*a.

While in the region of background aerosols ( 7 310212

*G b*aG 10210cm21sr21 at

*694 nm) all relative errors range between 40 and 50%, dS*a*OS*adescends below 40% for

*volcanic/STS PSC conditions (b*aB 1029cm21sr21) and values of 10–15% in the heavy

TABLE*II. – Coefficients of logarithmic parabolic fits*(*eq. (4)*)*to model-derived average values of*

*the variables (Var): surface area S*a( cm2Ocm3*), volume V*a( cm3Ocm3*), extinction s*a( cm21),

*extinction-to-backscatter ratio R*eb*4 s*a*Ob*a*( sr ) and effective radius r*eff*( cm ) as a function of*

*backscatter cross-section b*a( cm21sr21*) at 694 and 532 nm. b*min*and b*max( cm21sr21*) define the*

*region over which the fit was computed. The parabolic regression correlation coefficients r*
*indicate quality of the fit.*

Run Var *b*min *b*max *a*0 *a*1 *a*2 *r*

694
532
*S*a
*S*a
0.10 Q 10211
0.17 Q 10211
0.18 Q 10207
0.23 Q 10207
1.8665
1.8671
1.2892
1.3027
0.0333
0.0335
0.9997
0.9998
694
532
*V*a
*V*a
0.10 Q 10211
0.17 Q 10211
0.18 Q 10207
0.23 Q 10207 20.2304_{20.1023}
1.6024
1.6415
0.0342
0.0352
0.9999
0.9999
694
532
*s*a
*s*a
0.10 Q 10211
0.17 Q 10211
0.18 Q 10207
0.23 Q 10207
23.8894
24.8636
20.1393
20.3123
20.0576
20.0655
0.9999
1.0000
694
532
*s*a*Ob*a
*s*a*Ob*a
0.10 Q 10211
0.17 Q 10211
0.18 Q 10207
0.23 Q 10207
23.8809
24.9027
21.1386
21.3221
20.0577
20.0661
0.9717
0.9940
694
532
*r*eff
*r*eff
0.10 Q 10211
0.17 Q 10211
0.18 Q 10207
0.23 Q 10207 22.1843_{22.0104}
0.1954
0.2345
20.0045
20.0028
0.9994
0.9990

*volcanic/ice PSC conditions (b*aB 1028cm21sr21). Both Ruby-lidar and 532 nm surface

estimates are then affected by smaller errors in the presence of larger aerosols. This
behaviour differs from the one of particle counters, whose errors increase with the
*lowering in the number concentrations, i.e. for larger particles [23]. In this respect,*
*when evaluating Pinatubo aerosols surface area, Deshler et al. [17] reported optical*
counter average errors to range between 10 and 20%, with maxima of 60%. Therefore,
*expected errors of S*aestimates at both 694 and 532 nm wavelengths well compare with

*the ones characterizing in situ, particle counter observations.*

**4**.*2. Aerosol volume. – Average points of the relationships V*a *vs. b*a and relevant

*errors dV*a*OV*a*vs. b*aare plotted in figs. 2a and 2b, respectively. All points in fig. 2a are

well approximated by the second-order polynomial fits of eq. (4), plotted as a solid line.
Fit parameters and boundaries are reported in table II. Similarly to backscatter
cross-sections, particles volume spans 4 orders of magnitude. This is the largest
dynamical range amongst all the parameters investigated. For background aerosols,
*the 694 nm curve shows the typical sulphates volume V*a*E 0.1 mm*3cm23, which grows

*to V*a*D 1 mm*3cm23 in volcanic/PSC conditions.

Errors of volume estimates (fig. 2b) follow patterns opposite to the surface area
ones. In the region of background aerosols, errors of less than 20% point at volume
*estimates as more accurate than surface area ones. However, dV*a*OV*a values increase

(to approximately 25% at 694 nm) in heavy volcanic/ice PSC conditions. Overall,
Ruby-lidar volume estimates are affected by errors slightly lower than at 532 nm. At both
*wavelengths errors remain comparable to those reported for in situ particle counters*
(10-20% on average [17]).

**4**.*3. Extinction-to-backscatter ratio. – Average value points of the *
*extinction-to-backscatter ratio, R*eb*4 s*a*Ob*a *and relevant errors dR*eb*OR*eb *as a function of b*a are

*plotted in figs. 3a and 3b, respectively. In fig. 3a the parabolic fits to R*ebare also plotted

*as solid lines. The relevant coefficients are provided as variable s*a*Ob*ain table II. Up to

*approximately b*a4 3 3 10211cm21sr21*, values of R*eb are pretty similar at both

wavelengths. Beyond that point the two curves separate, the ratio being smaller the
*shorter the wavelength. Maxima of approximately R*eb*4 56 and R*eb4 51 sr are reached

at 694 and 532 nm, respectively. The two curves tend to converge again in the large
*cross-sections limit. In the case of volcanic aerosols or PSC (b*aF 1029 cm21sr21), both

*plots show R*eb *to decrease for increasing b*a, in good agreement with the behavior of

*R*ebat 532 nm as reported by Jager and Hofmann [21] and with the vertically resolved,

*R*eb*profiles of the Pinatubo cloud obtained by Ansmann et al. [24] at 308 nm. In typical*

*volcanic conditions, R*eb at 694 and 532 nm do not differ by more than 10%. However,

*when passing from background to heavy volcanic conditions, R*eb undergoes a change

*larger than 50%. Such behavior demonstrates the importance of employing suitable R*eb

values when inverting and comparing lidar observations taken in different conditions
and at different wavelengths. Correlation coefficients reported in table II show that,
*being a composed parameter, the quality of parabolic fits to the R*eb*vs. b*arelationship

*is somewhat poorer than for the other parameters. However, relative errors of R*eb

estimates at 694 nm (fig. 3b) are generally lower than 35%, and reach a minimum of
20–25% in the regions of background and heavy volcanic/ice PSC particles. Error
patterns are pretty similar at both 694 and 532 nm wavelengths. Altogether, model
*accuracy is consistent with the values (15–50%) characterizing determination of R*ebby

*Fig. 2. – (a): Average value points of the relationships V*a*vs. b*acomputed at 694 and 532 nm. Solid

lines show the log-log, second-order polynomial fit to the relevant points. Fit parameters are
*reported in table II. (b): Relative errors dV*a*OV*a *( dV*a*4 1 s) of fit estimates presented in (a).*

*Fig. 3. – (a): Average value points of the relationships R*eb*vs. b*acomputed at 694 and 532 nm. Solid

lines show the log-log, second-order polynomial fit to the relevant points. Fit parameters are
*reported in table II. (b): Relative errors dR*eb*OR*eb *( dR*eb*4 1 s) of fit estimates presented in (a).*

*Fig. 4. – (a): Average value points of the relationships s*a*vs. b*acomputed at 694 and 532 nm. Solid

lines show the log-log, second-order polynomial fit to the relevant points. Fit parameters are
*reported in table II. (b): Relative errors ds*a*Os*a *( ds*a*4 1 s) of fit estimates presented in (a).*

*Fig. 5. – (a): Average value points of the relationships r*eff*vs. b*acomputed at 694 and 532 nm. Solid

lines show the log-log, second-order polynomial fit to the relevant points. Fit parameters are
*reported in table II. (b): Relative errors dr*eff*Or*eff *( dr*eff*4 1 s) of fit estimates presented in (a).*

*Together with the lidar relevant R*eb ratio, it is useful to present the direct

relationship between extinction and backscatter cross-sections obtained by the model.
In fact, such link allows direct comparison between lidar and extinction observations.
*Average points of the s*a *vs. b*arelationship and relevant errors are plotted in figs. 4a

*and 4b, respectively. In table II are reported as variable s*a *the coefficients axE* of the

*second-order polynomial fits to the extinction vs. backscatter relationships drawn as*
*solid lines in fig. 4a. These plots show that at both wavelengths the link between s*aand

*b*a is be quite similar in the region of background aerosol, while some differences

appear when particles grow larger. These results show that direct inference of aerosol extinction from lidar observations is characterized by an error oscillating between 20 and 35% all over the range of observable particles (fig. 4b).

**4**.*4. Effective radius. – Points of average relationships between the distribution*
*effective radius r*eff *and b*a *are plotted in fig. 5a. Relevant errors dr*eff*/r*eff are shown in

*fig. 5b. When switching from background to volcanic/PSC conditions, r*eff increases

*approximately from 0.15 to 0.6 mm. Such behavior is in good agreement with*
observations reported by several authors after the Mt. Pinatubo eruption [9]. The
second-order polynomial fits (solid lines in fig. 5a) follow a quasi-linear behaviour.
Relevant parameters are presented in table II. In most aerosol conditions, relative
errors shown in fig. 5b range between 40 and 50%, indicating the effective radius as the
*distribution parameter suffering the highest variability. However, Russell et al. [9]*
*show that inference of r*eff by means of various remote-sensing techniques is

*characterized by errors ranging between 20 and 100%, i.e. even larger than the*
*present-model ones. Errors of in situ observations are not presented in [9]. In general,*
larger estimate errors and small dynamical range between background and
volcanic/PSC conditions make the distribution effective radius a variable less
favourable than the previous ones for characterizing stratospheric aerosols on the basis
of lidar observations.

**5. – Conclusions**

Functional relationships for estimating stratospheric aerosol surface area, volume,
extinction-to-backscatter ratio, extinction, and effective radius from single-wavelength,
694 nm Ruby-lidar measurements have been determined. These relationships have
*been obtained computing Mie scattering properties (b*a*, s*a) of sets of 10 000 aerosol

distributions and compositions, whose parameters were randomly generated according to boundary conditions derived from experimentally observed size distributions. These simulated aerosols are representative of worldwide stratospheric conditions including from background to postvolcanic sulphate particles and liquid polar stratospheric clouds (STS). Analytic expressions describing such properties have been derived from least-squares fitting of the average relationships linking the investigated parameters and aerosol backscatter. In log-log coordinates, these average points are well fitted by a second-order polynomial curve. Results have been compared to the ones obtained at 532 nm by the original optical model [11]. Functional relationships and relevant errors were found to follow similar patterns at both wavelengths.

Relative errors of the optical model at 694 nm range between 15 and 45% for surface area, being smaller at larger cross-sections. In the case of volume estimates, errors are of the order of 20%, slightly increasing in heavy volcanic conditions. Errors

characterizing extinction-to-backscatter ratio and extinction estimates oscillate in the
20–35% range, and minimize in heavy volcanic/PSC conditions. At all wavelengths,
these errors are comparable to the ones characterizing measurements obtained by
*operational, in situ techniques. Effective radius estimates suffer from a small*
dynamical range of the parameter and relative errors of 40–55%. These conditions
*make r*eff a less favourable output of the model, characterized by errors of magnitude

similar to the one of indirect techniques. As surface area errors strongly decrease at
*larger backscatter cross-sections, i.e. in the presence of volcanic clouds and PSC,*
application of the model to Ruby-lidar observations provides a good tool for estimating
a parameter so important in ozone-depletion studies. In the case of aerosol volume, the
694 nm model allows a slightly better evaluation than the 532 nm one, confirming,
however, the good capability of the method at estimating aerosol volume and mass.
Inference of a composite parameter as the extinction-to-backscatter ratio is
*characterized by a slightly lower quality of the fits. However, as R*ebhalves in passing

from moderate to heavy volcanic/PSC conditions, use of the analytic relationships provided by the model allows more realistic assumptions than the one of constant ratio, often employed in these cases. As a general rule, model relative errors and fit quality indicate the Ruby laser as very well suited for estimating stratospheric aerosol physical properties by means of single-wavelength lidar observations.

* * *

This work was partly supported by the Italian Space Agency, ASI.

R E F E R E N C E S

[1] HANSENJ., SATOM., LACISA. and RUEDY*R., The missing climate forcing, Philos. Trans. R.*

**Soc. London, B, 352 (1997) 231-240.**

[2] WORLDMETEOROLOGICALORGANIZATION*(WMO), Scientific Assessment of Ozone Depletion:*

*1994, Report 37, Geneva, 1995.*

[3] MICHELANGELID. V., ALLENM., and YUNG*Y. L., El Chichon volcanic aerosols: Impact of*

**radiative, thermal, and chemical perturbations, J. Geophys. Res., 94 (1989) 18429-18443.**

[4] TURCOR. P., WHITTENR. C. and TOON*O. B., Stratospheric aerosols: Observation and theory,*

**Rev. Geophys., 20 (1982) 233-279.**

[5] MIDDLEBROOKA. M., IRACIL. T., MCNEILLL. S., KOEHLERB. G., SAASTADO. W., TOLBERT
M. A. and HANSON*D. R., FTIR studies of thin film H*2SO4OH2*O films: Formation, water*

**uptake, and solid-liquid phase changes, J. Geophys. Res., 98 (1993) 20473-20481.**

[6] KOOPT. and CARSLAW*K. S., Melting of H*2SO4*-4 H*2*O particles upon cooling: Implications*

**for polar stratospheric clouds, Science, 272 (1996) 1638-1641.**

[7] STEELE H. M. and HAMILL *P., Effects of temperature and humidity on the growth and*

**optical properties of sulfuric acid-water droplets in the stratosphere, J. Aerosol Sci., 12**

(1981) 517-528.

[8] YUEG. K., POOLEL. R., WANGP. H. and CHIOU*E. W., Stratospheric aerosol acidity, density*

*and refractive index deduced from SAGE II and NMC temperature data, J. Geophys. Res.,*

**99 (1994) 3727-3738.**

[9] RUSSELL P. B., LIVINGSTON J. M., PUESCHELR. F., BAUMANJ. J., POLLACKJ. B., BROOKS
S. L., HAMILLP., THOMASONL. W., STOWEL. L., DESHLERT., DUTTONE. G. and BERGSTROM
*R. W., Global to microscale evolution of the Pinatubo volcanic aerosol derived from diverse*

[10] MOLINAM. J., ZHANGR., WOOLDRIDGEP. J., MCMAHONJ. R., KIMJ. E., CHANGH. Y. and
BEYER*K. D., Physical chemistry of the H*2SO4OHNO3OH2*O system: Implications for polar*

**stratospheric clouds, Science, 261 (1993) 1418-1423.**

[11] GOBBI *G. P., Lidar estimation of stratospheric aerosol properties: Surface, volume and*

**extinction to backscatter ratio, J. Geophys. Res., 100 (1995) 11219-11235.**

[12] COLLIS R. T. H. and RUSSELL *P. B., Lidar measurement of particle and gases by elastic*

*backscattering and differential absorption, in Laser Monitoring of the Atmosphere, edited*

by E. D. HINKLEY(Springer-Verlag, New York), 1976 pp. 71-145.

[13] WINKER D. M. and OSBORN *M. T., Airborne lidar observations of the Pinatubo volcanic*

**plume, Geophys. Res. Lett., 19 (1992) 167-170.**

[14] GOBBI G. P., CONGEDUTI F. and ADRIANI *A., Early stratospheric effects of the Pinatubo*

**eruption, Geophys. Res. Lett., 19 (1992) 997-1000.**

[15] GOBBI G. P., DI DONFRANCESCO G. and ADRIANI *A., Physical properties of stratospheric*

**clouds during the Antarctic winter of 1995, J. Geophys. Res., 103 (1998) 10859-10873.**

[16] RUSSELLP. B., SWISSLERT. J., MCCORMICKM. P., CHUW. P., LIVINGSTONJ. M. and PEPIN
*T. J., Satellite and correlative measurements of the stratospheric aerosol, I, An optical*

**model for data conversion, J. Atmos. Sci., 38 (1981) 1279-1294.**

[17] DESHLERT., JOHNSON B. J. and ROZIER*W. R., Balloonborne measurements of Pinatubo*

*aerosol during 1991 and 1992 at 41N: Vertical profiles, size distribution, and volatility,*
**Geophys. Res. Lett., 20 (1993) 1435-1438.**

[18] PINNICKR. G., ROSENJ. M. and HOFMANN*D. J., Stratospheric aerosol measurements, III,*

**Optical model calculations, J. Atmos. Sci., 33 (1976) 304-313.**

[19] HOFMANND. J. and ROSEN*J. M., Stratospheric sulfuric acid fraction and mass estimate for*

**the 1982 volcanic eruption of El Chichon, Geophys. Res. Lett., 10 (1983) 313-316.**

[20] SNETSINGERK. G., FERRYG. V., RUSSELLP. B., PUESCHELR. F. and OBERBECK*V. R., Effects*

**of the El Chichon on stratospheric aerosols, late 1982 to early 1984, J. Geophys. Res., 92**

(1987) 761-771.

[21] JAGERH. and HOFMANN*D. J., Midlatitude lidar backscatter to mass, area, and extinction*

**conversion model based on in situ aerosol measurements from 1980 to 1987, Appl. Opt., 30**

(1991) 127-138.

[22] TURCOR. P. and YU*F., Aerosol invariance in expanding coagulating plumes, Geophys. Res.*

**Lett., 24 (1997) 1223-1226.**

[23] HOFMANN D. J., ROSEN J. M., HARDER J. W. and HEREFORD *J. V., Balloon-borne*

*measurements of aerosol, condensation nuclei, and cloud particles in the stratosphere at*
**McMurdo Station, Antarctica, during the spring of 1987, J. Geophys. Res., 94 (1989)**

11253-11269.

[24] ANSMANNA., WANDINGERU. and WEITKAMP*C., One-year observations of Mount-Pinatubo*

**aerosol with an advanced raman lidar over Germany at 53.5N, Geophys. Res. Lett., 20 (1993)**